TY - JOUR
T1 - A p-adic analogue of a formula of Ramanujan
AU - McCarthy, Dermot
AU - Osburn, Robert
N1 - Funding Information:
Acknowledgements. The first author would like to thank the UCD Ad Astra Research Scholarship programme for its financial support. The second author thanks the Institut des Hautes Études Scientifiques for their hospitality and support during the preparation of this paper.
PY - 2008/12
Y1 - 2008/12
N2 - During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured p-adic analogues to such formulae. Using a combination of ordinary and Gaussian hypergeometric series, we prove one of these conjectures.
AB - During his lifetime, Ramanujan provided many formulae relating binomial sums to special values of the Gamma function. Based on numerical computations, Van Hamme recently conjectured p-adic analogues to such formulae. Using a combination of ordinary and Gaussian hypergeometric series, we prove one of these conjectures.
KW - Gaussian hypergeometric series
KW - Supercongruences
UR - http://www.scopus.com/inward/record.url?scp=58149129110&partnerID=8YFLogxK
U2 - 10.1007/s00013-008-2828-0
DO - 10.1007/s00013-008-2828-0
M3 - Article
AN - SCOPUS:58149129110
VL - 91
SP - 492
EP - 504
JO - Archiv der Mathematik
JF - Archiv der Mathematik
SN - 0003-889X
IS - 6
ER -